1. Field of the Invention
The present invention relates to an image signal processing apparatus for reading an original image and processing the thus obtained electric signals for use in a facsimile apparatus or the like, and more particularly such image signal processing apparatus utilizing a dither method for processing continuous tone in said original image.
2. Description of the Prior Art
The so-called dither method is already known for reproducing tonal rendition in an image reproducing apparatus only capable of producing a binary image composed of image areas and nonimage area such as black and white. This method is based on comparing, in digitizing the density signals obtained from the original image with a comparator, said density signals with reference voltages successively varied for example in 16 steps instead of a fixed reference voltage to obtain 17 different black-to-white area ratios, thereby reproducing 17 different densities utilizing the integrating effect of human eyes. In said method the 16 different reference voltages are so applied as to minimize the length of the external perimeter of pixels corresponding to said reference voltages in order to facilitate the integrating effect of human eyes. For example, if each pixel is square-shaped, said pixels are arranged as a square or a matrix of 4.times.4 pixels, which is called a dither matrix representing 16 comparison levels. Said 16 levels are assigned in an appropriate order to 4.times.4 pixels constituting said dither matrix to provide 17 combinations of black and white areas corresponding to 17 different densities.
Said assignment of 16 levels to the 4.times.4 pixels can be made in various manners, mathematically as many as: EQU .sub.16 P.sub.16 =16!.apprxeq.2.times.10 .sup.13 ( 1)
but one of the theoretically best arrangements of said levels would be the method proposed by Judis to maximize the spatial frequency of said arrangement. In this method an n.times.n dither matrix D.sup.n where n is a power of 2 is given by: ##EQU1## where U.sup.n is an n.times.n matrix of which the elements are all 1.
This method is based on the integrating effect of human eyes and provides a good resolving power even when the original image shows change in density with a relatively high spatial frequency, but the tonal rendition becomes deteriorated if the printer is unable to accurately reproduce each pixel.
More specifically, in case the resolving power of the printer represented by the modulation transfer function does not reach 1.0 at a spatial frequency equal to twice the Nyquist frequency f.sub.N, the reflective density of the obtained print becomes aberrated from the theoretical value represented by: ##EQU2## wherein D is the reflective density, B black-level reflective density, W white-level reflective density and P probability of presence of black pixels.
In such case the printer is unable to accurately print each pixel, and the reproduced image shows deteriorated tonal rendition with obscure boundaries between black areas and white areas, in comparison with the original image.
In case the printer is incapable of reproducing minimum dots, the tonal rendition can be made optimum, quite contrary to Judis' method, by an order of arrangement of the aforementioned levels so as to minimize the spatial frequency in the dither matrix. In this method the tonal rendition is improved since the image components of higher spatial frequencies are reduced in the reproduced image and the image reproduction is conducted principally in a part of printer performance where the resolving power (modulation transfer function) is high. In such case, however, the resolving power of the reproduced image is deteriorated due to the reduced spatial frequency of the dither matrix.
As explained above, the improvement in the tonal rendition and that in the resolving power are mutually contradictory requirements in the case that the printer is unable to satisfactorily reproduce the minimum dots, and a level arrangement in the dither matrix simultaneously satisfying these requirements has not been found.